#install.packages("forecast")
#install.packages("plotly")
#install.packages("tidyr")
#install.packages("dplyr")
library(forecast)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
data(EuStockMarkets)
summary(EuStockMarkets)
##       DAX            SMI            CAC            FTSE     
##  Min.   :1402   Min.   :1587   Min.   :1611   Min.   :2281  
##  1st Qu.:1744   1st Qu.:2166   1st Qu.:1875   1st Qu.:2843  
##  Median :2141   Median :2796   Median :1992   Median :3247  
##  Mean   :2531   Mean   :3376   Mean   :2228   Mean   :3566  
##  3rd Qu.:2722   3rd Qu.:3812   3rd Qu.:2274   3rd Qu.:3994  
##  Max.   :6186   Max.   :8412   Max.   :4388   Max.   :6179
class(EuStockMarkets)
## [1] "mts"    "ts"     "matrix"
par(mfrow=c(4,1))

x <- seq_len(nrow(EuStockMarkets))
for (i in seq_len(ncol(EuStockMarkets))) {
    y <- EuStockMarkets[,i]
    heading <- colnames(EuStockMarkets)[i]
    plot(x, y, type="n", main = heading, xaxt = "n")
    lines(x, EuStockMarkets[,i])
    years <- as.integer(time(EuStockMarkets))
    tick.posis <- seq(10, length(years), by = 100)
    axis(1, at = tick.posis, las = 2, labels = years[tick.posis])
}

plot(EuStockMarkets)

library(plotly)
## Loading required package: ggplot2
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
library(tidyr)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
stocks <- as.data.frame(EuStockMarkets) %>%
  gather(index, price) %>%
  mutate(time = rep(time(EuStockMarkets), 4))
plot_ly(stocks, x = ~time, y = ~price, color = ~index, mode = "lines")
## No trace type specified:
##   Based on info supplied, a 'scatter' trace seems appropriate.
##   Read more about this trace type -> https://plotly.com/r/reference/#scatter
ftse=(EuStockMarkets[,4])
plot(ftse)

components.ts = decompose(ftse)
plot(components.ts)

fit_ftse <- auto.arima(ftse, trace=TRUE)
## 
##  Fitting models using approximations to speed things up...
## 
##  ARIMA(2,1,2)(1,0,1)[260] with drift         : Inf
##  ARIMA(0,1,0)             with drift         : 17994.59
##  ARIMA(1,1,0)(1,0,0)[260] with drift         : Inf
##  ARIMA(0,1,1)(0,0,1)[260] with drift         : Inf
##  ARIMA(0,1,0)                                : 17997.78
##  ARIMA(0,1,0)(1,0,0)[260] with drift         : Inf
##  ARIMA(0,1,0)(0,0,1)[260] with drift         : Inf
##  ARIMA(0,1,0)(1,0,1)[260] with drift         : Inf
##  ARIMA(1,1,0)             with drift         : 17968.54
##  ARIMA(1,1,0)(0,0,1)[260] with drift         : Inf
##  ARIMA(1,1,0)(1,0,1)[260] with drift         : Inf
##  ARIMA(2,1,0)             with drift         : 17970.46
##  ARIMA(1,1,1)             with drift         : 17969.53
##  ARIMA(0,1,1)             with drift         : 17966.98
##  ARIMA(0,1,1)(1,0,0)[260] with drift         : Inf
##  ARIMA(0,1,1)(1,0,1)[260] with drift         : Inf
##  ARIMA(0,1,2)             with drift         : 17968.91
##  ARIMA(1,1,2)             with drift         : Inf
##  ARIMA(0,1,1)                                : 17969.15
## 
##  Now re-fitting the best model(s) without approximations...
## 
##  ARIMA(0,1,1)             with drift         : 17973.84
## 
##  Best model: ARIMA(0,1,1)             with drift
forecaste_ftse <- forecast(fit_ftse, 150)
plot(forecaste_ftse, main = "Graph with forecasting of ftse",col.main = "darkgreen") 

print(forecaste_ftse)
##          Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## 1998.650       5464.642 5425.690 5503.594 5405.070 5524.214
## 1998.654       5466.263 5407.555 5524.970 5376.477 5556.048
## 1998.658       5467.883 5394.563 5541.204 5355.749 5580.017
## 1998.662       5469.504 5384.033 5554.974 5338.788 5600.220
## 1998.665       5471.124 5375.028 5567.221 5324.157 5618.091
## 1998.669       5472.745 5367.086 5578.404 5311.153 5634.337
## 1998.673       5474.366 5359.940 5588.791 5299.367 5649.364
## 1998.677       5475.986 5353.420 5598.552 5288.537 5663.435
## 1998.681       5477.607 5347.408 5607.806 5278.484 5676.729
## 1998.685       5479.227 5341.819 5616.636 5269.079 5689.376
## 1998.688       5480.848 5336.590 5625.106 5260.224 5701.472
## 1998.692       5482.468 5331.671 5633.266 5251.844 5713.093
## 1998.696       5484.089 5327.025 5641.153 5243.881 5724.298
## 1998.700       5485.710 5322.620 5648.800 5236.285 5735.135
## 1998.704       5487.330 5318.429 5656.232 5229.018 5745.643
## 1998.708       5488.951 5314.431 5663.470 5222.046 5755.855
## 1998.712       5490.571 5310.609 5670.534 5215.343 5765.800
## 1998.715       5492.192 5306.947 5677.437 5208.884 5775.500
## 1998.719       5493.813 5303.431 5684.194 5202.650 5784.976
## 1998.723       5495.433 5300.051 5690.816 5196.622 5794.245
## 1998.727       5497.054 5296.795 5697.313 5190.784 5803.323
## 1998.731       5498.674 5293.655 5703.694 5185.124 5812.225
## 1998.735       5500.295 5290.623 5709.967 5179.630 5820.960
## 1998.738       5501.916 5287.692 5716.139 5174.290 5829.542
## 1998.742       5503.536 5284.856 5722.216 5169.094 5837.978
## 1998.746       5505.157 5282.109 5728.204 5164.035 5846.279
## 1998.750       5506.777 5279.446 5734.109 5159.104 5854.451
## 1998.754       5508.398 5276.862 5739.934 5154.294 5862.502
## 1998.758       5510.019 5274.353 5745.684 5149.600 5870.438
## 1998.762       5511.639 5271.915 5751.363 5145.013 5878.265
## 1998.765       5513.260 5269.545 5756.975 5140.530 5885.989
## 1998.769       5514.880 5267.239 5762.522 5136.146 5893.615
## 1998.773       5516.501 5264.995 5768.007 5131.855 5901.147
## 1998.777       5518.122 5262.809 5773.435 5127.654 5908.589
## 1998.781       5519.742 5260.678 5778.806 5123.538 5915.946
## 1998.785       5521.363 5258.602 5784.124 5119.504 5923.221
## 1998.788       5522.983 5256.576 5789.391 5115.549 5930.418
## 1998.792       5524.604 5254.600 5794.608 5111.669 5937.539
## 1998.796       5526.225 5252.671 5799.778 5107.861 5944.588
## 1998.800       5527.845 5250.788 5804.902 5104.123 5951.568
## 1998.804       5529.466 5248.948 5809.983 5100.451 5958.480
## 1998.808       5531.086 5247.151 5815.022 5096.845 5965.328
## 1998.812       5532.707 5245.394 5820.020 5093.300 5972.114
## 1998.815       5534.328 5243.677 5824.979 5089.815 5978.840
## 1998.819       5535.948 5241.997 5829.899 5086.389 5985.508
## 1998.823       5537.569 5240.354 5834.784 5083.018 5992.120
## 1998.827       5539.189 5238.747 5839.632 5079.702 5998.677
## 1998.831       5540.810 5237.173 5844.447 5076.438 6005.182
## 1998.835       5542.431 5235.633 5849.228 5073.225 6011.637
## 1998.838       5544.051 5234.126 5853.977 5070.061 6018.042
## 1998.842       5545.672 5232.649 5858.695 5066.945 6024.399
## 1998.846       5547.292 5231.203 5863.382 5063.875 6030.710
## 1998.850       5548.913 5229.786 5868.040 5060.851 6036.975
## 1998.854       5550.534 5228.398 5872.669 5057.870 6043.197
## 1998.858       5552.154 5227.038 5877.270 5054.932 6049.376
## 1998.862       5553.775 5225.705 5881.845 5052.035 6055.514
## 1998.865       5555.395 5224.398 5886.393 5049.179 6061.612
## 1998.869       5557.016 5223.117 5890.915 5046.362 6067.670
## 1998.873       5558.637 5221.861 5895.412 5043.583 6073.690
## 1998.877       5560.257 5220.629 5899.885 5040.841 6079.673
## 1998.881       5561.878 5219.421 5904.334 5038.136 6085.620
## 1998.885       5563.498 5218.237 5908.760 5035.466 6091.531
## 1998.888       5565.119 5217.074 5913.164 5032.831 6097.407
## 1998.892       5566.740 5215.934 5917.545 5030.229 6103.250
## 1998.896       5568.360 5214.816 5921.905 5027.661 6109.060
## 1998.900       5569.981 5213.718 5926.243 5025.124 6114.837
## 1998.904       5571.601 5212.641 5930.561 5022.619 6120.583
## 1998.908       5573.222 5211.585 5934.859 5020.145 6126.299
## 1998.912       5574.843 5210.547 5939.138 5017.701 6131.984
## 1998.915       5576.463 5209.530 5943.397 5015.287 6137.640
## 1998.919       5578.084 5208.531 5947.637 5012.901 6143.267
## 1998.923       5579.704 5207.550 5951.859 5010.543 6148.865
## 1998.927       5581.325 5206.587 5956.063 5008.213 6154.437
## 1998.931       5582.946 5205.643 5960.249 5005.910 6159.981
## 1998.935       5584.566 5204.715 5964.417 5003.634 6165.498
## 1998.938       5586.187 5203.805 5968.569 5001.384 6170.990
## 1998.942       5587.807 5202.911 5972.704 4999.159 6176.456
## 1998.946       5589.428 5202.033 5976.823 4996.959 6181.897
## 1998.950       5591.049 5201.171 5980.926 4994.783 6187.314
## 1998.954       5592.669 5200.326 5985.013 4992.631 6192.707
## 1998.958       5594.290 5199.495 5989.084 4990.504 6198.076
## 1998.962       5595.910 5198.680 5993.141 4988.399 6203.422
## 1998.965       5597.531 5197.879 5997.183 4986.317 6208.745
## 1998.969       5599.152 5197.093 6001.210 4984.257 6214.046
## 1998.973       5600.772 5196.322 6005.222 4982.219 6219.326
## 1998.977       5602.393 5195.564 6009.221 4980.202 6224.583
## 1998.981       5604.013 5194.821 6013.206 4978.207 6229.820
## 1998.985       5605.634 5194.090 6017.177 4976.233 6235.035
## 1998.988       5607.255 5193.374 6021.135 4974.278 6240.231
## 1998.992       5608.875 5192.670 6025.080 4972.344 6245.406
## 1998.996       5610.496 5191.979 6029.012 4970.430 6250.561
## 1999.000       5612.116 5191.301 6032.931 4968.535 6255.697
## 1999.004       5613.737 5190.636 6036.838 4966.660 6260.814
## 1999.008       5615.358 5189.982 6040.733 4964.803 6265.913
## 1999.012       5616.978 5189.341 6044.615 4962.964 6270.992
## 1999.015       5618.599 5188.712 6048.485 4961.144 6276.054
## 1999.019       5620.219 5188.094 6052.344 4959.341 6281.097
## 1999.023       5621.840 5187.488 6056.191 4957.557 6286.123
## 1999.027       5623.461 5186.894 6060.027 4955.789 6291.132
## 1999.031       5625.081 5186.310 6063.852 4954.039 6296.123
## 1999.035       5626.702 5185.738 6067.666 4952.306 6301.098
## 1999.038       5628.322 5185.176 6071.468 4950.589 6306.056
## 1999.042       5629.943 5184.625 6075.261 4948.888 6310.998
## 1999.046       5631.564 5184.085 6079.042 4947.204 6315.923
## 1999.050       5633.184 5183.555 6082.813 4945.536 6320.833
## 1999.054       5634.805 5183.035 6086.574 4943.883 6325.727
## 1999.058       5636.425 5182.525 6090.325 4942.245 6330.605
## 1999.062       5638.046 5182.026 6094.066 4940.623 6335.469
## 1999.065       5639.667 5181.536 6097.797 4939.016 6340.317
## 1999.069       5641.287 5181.056 6101.519 4937.424 6345.150
## 1999.073       5642.908 5180.585 6105.231 4935.846 6349.969
## 1999.077       5644.528 5180.124 6108.933 4934.283 6354.774
## 1999.081       5646.149 5179.672 6112.626 4932.734 6359.564
## 1999.085       5647.770 5179.229 6116.310 4931.198 6364.341
## 1999.088       5649.390 5178.795 6119.985 4929.677 6369.103
## 1999.092       5651.011 5178.370 6123.651 4928.170 6373.852
## 1999.096       5652.631 5177.954 6127.308 4926.675 6378.587
## 1999.100       5654.252 5177.547 6130.957 4925.195 6383.309
## 1999.104       5655.872 5177.148 6134.597 4923.727 6388.018
## 1999.108       5657.493 5176.758 6138.228 4922.272 6392.714
## 1999.112       5659.114 5176.376 6141.851 4920.830 6397.397
## 1999.115       5660.734 5176.003 6145.466 4919.401 6402.068
## 1999.119       5662.355 5175.637 6149.073 4917.984 6406.725
## 1999.123       5663.975 5175.280 6152.671 4916.580 6411.371
## 1999.127       5665.596 5174.930 6156.262 4915.188 6416.005
## 1999.131       5667.217 5174.589 6159.844 4913.807 6420.626
## 1999.135       5668.837 5174.255 6163.419 4912.439 6425.235
## 1999.138       5670.458 5173.929 6166.987 4911.083 6429.833
## 1999.142       5672.078 5173.611 6170.546 4909.738 6434.419
## 1999.146       5673.699 5173.300 6174.098 4908.404 6438.994
## 1999.150       5675.320 5172.996 6177.643 4907.082 6443.557
## 1999.154       5676.940 5172.700 6181.180 4905.772 6448.109
## 1999.158       5678.561 5172.411 6184.710 4904.472 6452.650
## 1999.162       5680.181 5172.130 6188.233 4903.183 6457.180
## 1999.165       5681.802 5171.855 6191.749 4901.905 6461.699
## 1999.169       5683.423 5171.587 6195.258 4900.638 6466.207
## 1999.173       5685.043 5171.327 6198.760 4899.382 6470.705
## 1999.177       5686.664 5171.073 6202.255 4898.136 6475.192
## 1999.181       5688.284 5170.826 6205.743 4896.900 6479.669
## 1999.185       5689.905 5170.586 6209.224 4895.675 6484.136
## 1999.188       5691.526 5170.352 6212.699 4894.459 6488.592
## 1999.192       5693.146 5170.125 6216.168 4893.254 6493.038
## 1999.196       5694.767 5169.904 6219.629 4892.059 6497.475
## 1999.200       5696.387 5169.690 6223.085 4890.874 6501.901
## 1999.204       5698.008 5169.483 6226.534 4889.698 6506.318
## 1999.208       5699.629 5169.281 6229.976 4888.532 6510.725
## 1999.212       5701.249 5169.086 6233.413 4887.376 6515.123
## 1999.215       5702.870 5168.897 6236.843 4886.229 6519.511
## 1999.219       5704.490 5168.714 6240.267 4885.091 6523.890
## 1999.223       5706.111 5168.537 6243.685 4883.963 6528.260
smi=(EuStockMarkets[,2])
plot(smi)

components.ts = decompose(smi)
plot(components.ts)

fit_smi <- auto.arima(smi, trace=TRUE)
## 
##  Fitting models using approximations to speed things up...
## 
##  ARIMA(2,2,2)(1,0,1)[260]                    : Inf
##  ARIMA(0,2,0)                                : 20131.81
##  ARIMA(1,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(0,2,1)(0,0,1)[260]                    : Inf
##  ARIMA(0,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(0,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(0,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(1,2,0)                                : 19656.54
##  ARIMA(1,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(1,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(2,2,0)                                : 19471.95
##  ARIMA(2,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(2,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(2,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(3,2,0)                                : 19389.41
##  ARIMA(3,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(3,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(3,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(4,2,0)                                : 19351.77
##  ARIMA(4,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(4,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(4,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(5,2,0)                                : 19282.73
##  ARIMA(5,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(5,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(5,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(5,2,1)                                : Inf
##  ARIMA(4,2,1)                                : Inf
## 
##  Now re-fitting the best model(s) without approximations...
## 
##  ARIMA(5,2,0)                                : 19295.02
## 
##  Best model: ARIMA(5,2,0)
forecaste_smi <- forecast(fit_smi, 150)
plot(forecaste_smi, main = "Graph with forecasting of smi",col.main = "darkgreen") 

print(forecaste_smi)
##          Point Forecast        Lo 80     Hi 80        Lo 95     Hi 95
## 1998.650       7687.499   7631.83090  7743.168   7602.36172  7772.637
## 1998.654       7652.238   7563.18203  7741.293   7516.03889  7788.436
## 1998.658       7617.448   7495.74729  7739.148   7431.32291  7803.573
## 1998.662       7646.633   7490.80986  7802.457   7408.32188  7884.945
## 1998.665       7644.052   7451.92849  7836.176   7350.22426  7937.880
## 1998.669       7664.777   7434.10988  7895.444   7312.00220  8017.551
## 1998.673       7668.581   7393.15781  7944.004   7247.35772  8089.804
## 1998.677       7666.203   7344.07701  7988.329   7173.55370  8158.853
## 1998.681       7664.865   7294.12510  8035.604   7097.86750  8231.862
## 1998.685       7672.903   7251.52019  8094.287   7028.45340  8317.353
## 1998.688       7676.172   7202.08064  8150.262   6951.11208  8401.231
## 1998.692       7682.438   7153.62980  8211.246   6873.69566  8491.180
## 1998.696       7686.193   7100.28876  8272.097   6790.12987  8582.256
## 1998.700       7689.157   7044.30095  8334.014   6702.93465  8675.380
## 1998.704       7692.413   6986.80416  8398.023   6613.27722  8771.549
## 1998.708       7697.032   6928.89039  8465.173   6522.26091  8871.803
## 1998.712       7700.925   6868.50419  8533.346   6427.84717  8974.003
## 1998.715       7705.198   6806.79484  8603.602   6331.20874  9079.188
## 1998.719       7709.104   6743.00807  8675.200   6231.58780  9186.620
## 1998.723       7712.914   6677.51184  8748.316   6129.40315  9296.424
## 1998.727       7716.786   6610.50075  8823.071   6024.86874  9408.703
## 1998.731       7720.854   6542.13781  8899.570   5918.16313  9523.545
## 1998.735       7724.811   6472.14567  8977.476   5809.02475  9640.597
## 1998.738       7728.815   6400.71350  9056.917   5697.65897  9759.971
## 1998.742       7732.766   6327.76405  9137.769   5584.00075  9881.532
## 1998.746       7736.707   6253.37408  9220.040   5468.14514 10005.269
## 1998.750       7740.659   6177.59172  9303.727   5350.15378 10131.165
## 1998.754       7744.639   6100.45656  9388.822   5230.07875 10259.200
## 1998.758       7748.602   6021.94634  9475.258   5107.90983 10389.295
## 1998.762       7752.571   5942.10613  9563.036   4983.70379 10521.439
## 1998.765       7756.533   5860.94293  9652.122   4857.47840 10655.587
## 1998.769       7760.493   5778.48425  9742.501   4729.27228 10791.713
## 1998.773       7764.455   5694.75230  9834.158   4599.11778 10929.793
## 1998.777       7768.421   5609.76712  9927.076   4467.04453 11069.798
## 1998.781       7772.385   5523.53961 10021.231   4333.07273 11211.697
## 1998.785       7776.349   5436.09000 10116.609   4197.23151 11355.467
## 1998.788       7780.313   5347.43262 10213.193   4059.54372 11501.082
## 1998.792       7784.276   5257.58413 10310.968   3920.03432 11648.517
## 1998.796       7788.239   5166.55990 10409.919   3778.72658 11797.752
## 1998.800       7792.204   5074.37449 10510.033   3635.64270 11948.764
## 1998.804       7796.167   4981.04082 10611.294   3490.80294 12101.531
## 1998.808       7800.131   4886.57281 10713.689   3344.22829 12256.034
## 1998.812       7804.095   4790.98316 10817.206   3195.93831 12412.251
## 1998.815       7808.058   4694.28453 10921.832   3045.95230 12570.164
## 1998.819       7812.022   4596.48907 11027.555   2894.28881 12729.755
## 1998.823       7815.986   4497.60852 11134.363   2740.96576 12891.006
## 1998.827       7819.949   4397.65405 11242.245   2586.00035 13053.898
## 1998.831       7823.913   4296.63676 11351.189   2429.40948 13218.417
## 1998.835       7827.877   4194.56726 11461.186   2271.20940 13384.544
## 1998.838       7831.840   4091.45593 11572.225   2111.41598 13552.265
## 1998.842       7835.804   3987.31282 11684.295   1950.04458 13721.564
## 1998.846       7839.768   3882.14769 11797.388   1787.11013 13892.426
## 1998.850       7843.732   3775.97000 11911.493   1622.62713 14064.836
## 1998.854       7847.695   3668.78901 12026.601   1456.60969 14238.781
## 1998.858       7851.659   3560.61369 12142.704   1289.07155 14414.246
## 1998.862       7855.623   3451.45277 12259.792   1120.02609 14591.219
## 1998.865       7859.586   3341.31480 12377.858    949.48634 14769.686
## 1998.869       7863.550   3230.20805 12496.892    777.46498 14949.635
## 1998.873       7867.514   3118.14062 12616.887    603.97438 15131.053
## 1998.877       7871.477   3005.12041 12737.834    429.02663 15313.928
## 1998.881       7875.441   2891.15511 12859.727    252.63350 15498.249
## 1998.885       7879.405   2776.25225 12982.557     74.80647 15684.003
## 1998.888       7883.368   2660.41915 13106.318   -104.44321 15871.180
## 1998.892       7887.332   2543.66300 13231.001   -285.10459 16059.769
## 1998.896       7891.296   2425.99079 13356.601   -467.16696 16249.759
## 1998.900       7895.260   2307.40939 13483.110   -650.61982 16441.139
## 1998.904       7899.223   2187.92547 13610.521   -835.45295 16633.899
## 1998.908       7903.187   2067.54561 13738.828  -1021.65632 16828.030
## 1998.912       7907.151   1946.27621 13868.025  -1209.22012 17023.521
## 1998.915       7911.114   1824.12354 13998.105  -1398.13476 17220.363
## 1998.919       7915.078   1701.09375 14129.062  -1588.39084 17418.547
## 1998.923       7919.042   1577.19286 14260.891  -1779.97915 17618.063
## 1998.927       7923.005   1452.42676 14393.584  -1972.89069 17818.902
## 1998.931       7926.969   1326.80123 14527.137  -2167.11661 18021.055
## 1998.935       7930.933   1200.32194 14661.544  -2362.64825 18224.514
## 1998.938       7934.897   1072.99443 14796.799  -2559.47712 18429.270
## 1998.942       7938.860    944.82416 14932.896  -2757.59489 18635.315
## 1998.946       7942.824    815.81646 15069.831  -2956.99339 18842.641
## 1998.950       7946.788    685.97658 15207.599  -3157.66460 19051.240
## 1998.954       7950.751    555.30967 15346.193  -3359.60066 19261.103
## 1998.958       7954.715    423.82076 15485.609  -3562.79384 19472.224
## 1998.962       7958.679    291.51483 15625.843  -3767.23656 19684.594
## 1998.965       7962.642    158.39674 15766.888  -3972.92136 19898.206
## 1998.969       7966.606     24.47127 15908.741  -4179.84094 20113.053
## 1998.973       7970.570   -110.25687 16051.396  -4387.98811 20329.128
## 1998.977       7974.533   -245.78306 16194.850  -4597.35579 20546.423
## 1998.981       7978.497   -382.10277 16339.097  -4807.93705 20764.931
## 1998.985       7982.461   -519.21153 16484.133  -5019.72505 20984.647
## 1998.988       7986.425   -657.10495 16629.954  -5232.71309 21205.562
## 1998.992       7990.388   -795.77871 16776.555  -5446.89456 21427.671
## 1998.996       7994.352   -935.22857 16923.933  -5662.26297 21650.967
## 1999.000       7998.316  -1075.45035 17072.082  -5878.81193 21875.443
## 1999.004       8002.279  -1216.43994 17220.999  -6096.53516 22101.094
## 1999.008       8006.243  -1358.19329 17370.679  -6315.42645 22327.913
## 1999.012       8010.207  -1500.70642 17521.120  -6535.47973 22555.893
## 1999.015       8014.170  -1643.97541 17672.316  -6756.68900 22785.030
## 1999.019       8018.134  -1787.99640 17824.265  -6979.04834 23015.317
## 1999.023       8022.098  -1932.76558 17976.961  -7202.55195 23246.748
## 1999.027       8026.062  -2078.27921 18130.402  -7427.19410 23479.317
## 1999.031       8030.025  -2224.53361 18284.584  -7652.96915 23713.020
## 1999.035       8033.989  -2371.52513 18439.503  -7879.87153 23947.849
## 1999.038       8037.953  -2519.25019 18595.155  -8107.89577 24183.801
## 1999.042       8041.916  -2667.70526 18751.538  -8337.03646 24420.869
## 1999.046       8045.880  -2816.88686 18908.647  -8567.28829 24659.048
## 1999.050       8049.844  -2966.79157 19066.479  -8798.64601 24898.333
## 1999.054       8053.807  -3117.41600 19225.031  -9031.10445 25138.719
## 1999.058       8057.771  -3268.75681 19384.299  -9264.65850 25380.201
## 1999.062       8061.735  -3420.81071 19544.280  -9499.30313 25622.773
## 1999.065       8065.698  -3573.57446 19704.971  -9735.03338 25866.430
## 1999.069       8069.662  -3727.04487 19866.369  -9971.84436 26111.169
## 1999.073       8073.626  -3881.21876 20028.471 -10209.73123 26356.983
## 1999.077       8077.590  -4036.09302 20191.272 -10448.68924 26603.868
## 1999.081       8081.553  -4191.66459 20354.771 -10688.71367 26851.820
## 1999.085       8085.517  -4347.93042 20518.964 -10929.79989 27100.834
## 1999.088       8089.481  -4504.88753 20683.849 -11171.94332 27350.905
## 1999.092       8093.444  -4662.53294 20849.422 -11415.13943 27602.028
## 1999.096       8097.408  -4820.86375 21015.680 -11659.38376 27854.200
## 1999.100       8101.372  -4979.87707 21182.621 -11904.67190 28107.415
## 1999.104       8105.335  -5139.57005 21350.241 -12150.99950 28361.670
## 1999.108       8109.299  -5299.93989 21518.538 -12398.36225 28616.961
## 1999.112       8113.263  -5460.98381 21687.509 -12646.75592 28873.282
## 1999.115       8117.227  -5622.69906 21857.152 -12896.17631 29130.629
## 1999.119       8121.190  -5785.08293 22027.463 -13146.61927 29389.000
## 1999.123       8125.154  -5948.13275 22198.441 -13398.08070 29648.389
## 1999.127       8129.118  -6111.84588 22370.081 -13650.55658 29908.792
## 1999.131       8133.081  -6276.21969 22542.382 -13904.04289 30170.206
## 1999.135       8137.045  -6441.25161 22715.342 -14158.53568 30432.626
## 1999.138       8141.009  -6606.93909 22888.957 -14414.03106 30696.048
## 1999.142       8144.972  -6773.27959 23063.224 -14670.52517 30960.470
## 1999.146       8148.936  -6940.27063 23238.143 -14928.01418 31225.886
## 1999.150       8152.900  -7107.90974 23413.709 -15186.49433 31492.294
## 1999.154       8156.863  -7276.19448 23589.921 -15445.96188 31759.689
## 1999.158       8160.827  -7445.12244 23766.777 -15706.41315 32028.068
## 1999.162       8164.791  -7614.69124 23944.273 -15967.84450 32297.426
## 1999.165       8168.755  -7784.89851 24122.408 -16230.25232 32567.761
## 1999.169       8172.718  -7955.74193 24301.178 -16493.63303 32839.070
## 1999.173       8176.682  -8127.21919 24480.583 -16757.98312 33111.347
## 1999.177       8180.646  -8299.32800 24660.619 -17023.29909 33384.590
## 1999.181       8184.609  -8472.06612 24841.285 -17289.57749 33658.796
## 1999.185       8188.573  -8645.43130 25022.577 -17556.81491 33933.961
## 1999.188       8192.537  -8819.42134 25204.495 -17825.00796 34210.081
## 1999.192       8196.500  -8994.03404 25387.035 -18094.15331 34487.154
## 1999.196       8200.464  -9169.26726 25570.196 -18364.24764 34765.176
## 1999.200       8204.428  -9345.11884 25753.975 -18635.28768 35044.143
## 1999.204       8208.392  -9521.58667 25938.370 -18907.27018 35324.053
## 1999.208       8212.355  -9698.66864 26123.379 -19180.19194 35604.902
## 1999.212       8216.319  -9876.36269 26309.001 -19454.04979 35886.688
## 1999.215       8220.283 -10054.66675 26495.232 -19728.84058 36169.406
## 1999.219       8224.246 -10233.57880 26682.071 -20004.56119 36453.054
## 1999.223       8228.210 -10413.09681 26869.517 -20281.20855 36737.629
dax=(EuStockMarkets[,1])
plot(dax)

components.ts = decompose(dax)
plot(components.ts)

fit_dax <- auto.arima(dax, trace=TRUE)
## 
##  Fitting models using approximations to speed things up...
## 
##  ARIMA(2,2,2)(1,0,1)[260]                    : Inf
##  ARIMA(0,2,0)                                : 19475.21
##  ARIMA(1,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(0,2,1)(0,0,1)[260]                    : Inf
##  ARIMA(0,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(0,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(0,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(1,2,0)                                : 18963.57
##  ARIMA(1,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(1,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(2,2,0)                                : 18749.75
##  ARIMA(2,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(2,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(2,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(3,2,0)                                : 18635.06
##  ARIMA(3,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(3,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(3,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(4,2,0)                                : 18584.6
##  ARIMA(4,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(4,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(4,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(5,2,0)                                : 18495.78
##  ARIMA(5,2,0)(1,0,0)[260]                    : Inf
##  ARIMA(5,2,0)(0,0,1)[260]                    : Inf
##  ARIMA(5,2,0)(1,0,1)[260]                    : Inf
##  ARIMA(5,2,1)                                : 18223.75
##  ARIMA(5,2,1)(1,0,0)[260]                    : Inf
##  ARIMA(5,2,1)(0,0,1)[260]                    : Inf
##  ARIMA(5,2,1)(1,0,1)[260]                    : Inf
##  ARIMA(4,2,1)                                : Inf
##  ARIMA(5,2,2)                                : Inf
##  ARIMA(4,2,2)                                : Inf
## 
##  Now re-fitting the best model(s) without approximations...
## 
##  ARIMA(5,2,1)                                : Inf
##  ARIMA(5,2,0)                                : 18508.04
## 
##  Best model: ARIMA(5,2,0)
forecaste_dax <- forecast(fit_dax, 150)
plot(forecaste_dax, main = "Graph with forecasting of dax",col.main = "darkgreen") 

print(forecaste_dax)
##          Point Forecast       Lo 80     Hi 80        Lo 95     Hi 95
## 1998.650       5477.071  5432.02996  5522.113   5408.18642  5545.957
## 1998.654       5455.437  5385.72621  5525.148   5348.82337  5562.051
## 1998.658       5438.930  5345.83957  5532.020   5296.56051  5581.299
## 1998.662       5470.902  5353.45411  5588.349   5291.28107  5650.522
## 1998.665       5478.529  5334.55983  5622.498   5258.34723  5698.710
## 1998.669       5505.691  5333.18248  5678.199   5241.86212  5769.519
## 1998.673       5512.314  5306.11510  5718.513   5196.95988  5827.669
## 1998.677       5517.260  5276.48198  5758.037   5149.02196  5885.497
## 1998.681       5524.894  5248.36282  5801.426   5101.97581  5947.813
## 1998.685       5540.523  5226.76715  5854.279   5060.67485  6020.371
## 1998.688       5551.386  5198.74638  5904.026   5012.07011  6090.702
## 1998.692       5564.652  5171.57225  5957.732   4963.48846  6165.815
## 1998.696       5574.519  5139.17198  6009.867   4908.71301  6240.326
## 1998.700       5584.631  5105.76102  6063.500   4852.26279  6316.998
## 1998.704       5595.439  5071.76273  6119.116   4794.54513  6396.333
## 1998.708       5607.468  5037.67149  6177.265   4736.03925  6478.897
## 1998.712       5618.547  5001.31322  6235.781   4674.56945  6562.524
## 1998.715       5629.916  4963.98087  6295.852   4611.45597  6648.377
## 1998.719       5640.767  4924.86387  6356.669   4545.88789  6735.645
## 1998.723       5651.753  4884.71802  6418.789   4478.67404  6824.833
## 1998.727       5662.881  4843.55822  6482.203   4409.83510  6915.926
## 1998.731       5674.177  4801.42576  6546.928   4339.41932  7008.934
## 1998.735       5685.286  4757.98422  6612.588   4267.10015  7103.472
## 1998.738       5696.434  4713.48573  6679.383   4193.14411  7199.725
## 1998.742       5707.511  4667.83780  6747.183   4117.46828  7297.553
## 1998.746       5718.625  4621.18019  6816.069   4040.22809  7397.022
## 1998.750       5729.763  4573.51383  6886.012   3961.43262  7498.093
## 1998.754       5740.921  4524.85105  6956.990   3881.10266  7600.739
## 1998.758       5752.044  4475.15311  7028.934   3799.20816  7704.879
## 1998.762       5763.173  4424.47891  7101.867   3715.81718  7810.528
## 1998.765       5774.293  4372.82833  7175.758   3630.93759  7917.649
## 1998.769       5785.422  4320.23458  7250.610   3544.61107  8026.233
## 1998.773       5796.554  4266.70582  7326.403   3456.85286  8136.256
## 1998.777       5807.688  4212.25375  7403.123   3367.68162  8247.695
## 1998.781       5818.816  4156.88315  7480.749   3277.10896  8360.523
## 1998.785       5829.945  4100.61431  7559.276   3185.16182  8474.729
## 1998.788       5841.073  4043.45681  7638.690   3091.85605  8590.291
## 1998.792       5852.203  3985.42473  7718.982   2997.21186  8707.195
## 1998.796       5863.333  3926.52760  7800.139   2901.24452  8825.422
## 1998.800       5874.464  3866.77568  7882.152   2803.96987  8944.957
## 1998.804       5885.593  3806.17809  7965.007   2705.40246  9065.783
## 1998.808       5896.722  3744.74611  8048.698   2605.55878  9187.886
## 1998.812       5907.852  3682.48886  8133.214   2504.45299  9311.250
## 1998.815       5918.981  3619.41589  8218.547   2402.09950  9435.863
## 1998.819       5930.111  3555.53576  8304.686   2298.51159  9561.710
## 1998.823       5941.241  3490.85706  8391.624   2193.70237  9688.779
## 1998.827       5952.370  3425.38798  8479.352   2087.68447  9817.056
## 1998.831       5963.500  3359.13686  8567.862   1980.47049  9946.529
## 1998.835       5974.629  3292.11145  8657.147   1872.07234 10077.186
## 1998.838       5985.759  3224.31940  8747.198   1762.50169 10209.016
## 1998.842       5996.888  3155.76803  8838.009   1651.76977 10342.007
## 1998.846       6008.018  3086.46452  8929.571   1539.88756 10476.148
## 1998.850       6019.147  3016.41583  9021.879   1426.86570 10611.429
## 1998.854       6030.277  2945.62878  9114.925   1312.71461 10747.840
## 1998.858       6041.407  2874.10996  9208.703   1197.44438 10885.369
## 1998.862       6052.536  2801.86580  9303.207   1081.06484 11024.008
## 1998.865       6063.666  2728.90256  9398.429    963.58554 11163.746
## 1998.869       6074.795  2655.22633  9494.364    845.01583 11304.575
## 1998.873       6085.925  2580.84306  9591.007    725.36480 11446.485
## 1998.877       6097.054  2505.75855  9688.350    604.64132 11589.468
## 1998.881       6108.184  2429.97848  9786.390    482.85405 11733.514
## 1998.885       6119.314  2353.50835  9885.119    360.01145 11878.616
## 1998.888       6130.443  2276.35357  9984.533    236.12176 12024.765
## 1998.892       6141.573  2198.51941 10084.626    111.19305 12171.953
## 1998.896       6152.702  2120.01102 10185.394    -14.76681 12320.172
## 1998.900       6163.832  2040.83344 10286.830   -141.75012 12469.414
## 1998.904       6174.961  1960.99158 10388.931   -269.74933 12619.672
## 1998.908       6186.091  1880.49028 10491.692   -398.75710 12770.939
## 1998.912       6197.221  1799.33423 10595.107   -528.76620 12923.207
## 1998.915       6208.350  1717.52806 10699.172   -659.76958 13076.470
## 1998.919       6219.480  1635.07628 10803.883   -791.76033 13230.720
## 1998.923       6230.609  1551.98332 10909.235   -924.73168 13385.950
## 1998.927       6241.739  1468.25352 11015.224  -1058.67701 13542.155
## 1998.931       6252.868  1383.89111 11121.846  -1193.58981 13699.327
## 1998.935       6263.998  1298.90027 11229.096  -1329.46372 13857.460
## 1998.938       6275.128  1213.28509 11336.970  -1466.29250 14016.548
## 1998.942       6286.257  1127.04955 11445.465  -1604.07001 14176.584
## 1998.946       6297.387  1040.19760 11554.576  -1742.79025 14337.564
## 1998.950       6308.516   952.73308 11664.300  -1882.44732 14499.480
## 1998.954       6319.646   864.65978 11774.632  -2023.03544 14662.327
## 1998.958       6330.775   775.98142 11885.570  -2164.54893 14826.100
## 1998.962       6341.905   686.70164 11997.108  -2306.98221 14990.792
## 1998.965       6353.035   596.82402 12109.245  -2450.32981 15156.399
## 1998.969       6364.164   506.35208 12221.976  -2594.58634 15322.915
## 1998.973       6375.294   415.28928 12335.298  -2739.74651 15490.334
## 1998.977       6386.423   323.63902 12449.208  -2885.80514 15658.652
## 1998.981       6397.553   231.40463 12563.701  -3032.75710 15827.863
## 1998.985       6408.682   138.58939 12678.776  -3180.59739 15997.962
## 1998.988       6419.812    45.19655 12794.428  -3329.32106 16168.945
## 1998.992       6430.942   -48.77074 12910.654  -3478.92326 16340.807
## 1998.996       6442.071  -143.30934 13027.452  -3629.39922 16513.542
## 1999.000       6453.201  -238.41619 13144.818  -3780.74422 16687.146
## 1999.004       6464.330  -334.08825 13262.749  -3932.95366 16861.614
## 1999.008       6475.460  -430.32256 13381.242  -4086.02297 17036.943
## 1999.012       6486.589  -527.11618 13500.295  -4239.94768 17213.127
## 1999.015       6497.719  -624.46623 13619.904  -4394.72337 17390.161
## 1999.019       6508.849  -722.36987 13740.067  -4550.34571 17568.043
## 1999.023       6519.978  -820.82431 13860.781  -4706.81041 17746.767
## 1999.027       6531.108  -919.82678 13982.042  -4864.11327 17926.329
## 1999.031       6542.237 -1019.37458 14103.849  -5022.25012 18106.725
## 1999.035       6553.367 -1119.46502 14226.199  -5181.21689 18287.951
## 1999.038       6564.496 -1220.09548 14349.088  -5341.00954 18470.002
## 1999.042       6575.626 -1321.26336 14472.515  -5501.62410 18652.876
## 1999.046       6586.756 -1422.96610 14596.477  -5663.05665 18836.568
## 1999.050       6597.885 -1525.20117 14720.972  -5825.30334 19021.074
## 1999.054       6609.015 -1627.96609 14845.996  -5988.36036 19206.390
## 1999.058       6620.144 -1731.25840 14971.547  -6152.22395 19392.513
## 1999.062       6631.274 -1835.07568 15097.623  -6316.89042 19579.438
## 1999.065       6642.403 -1939.41555 15224.222  -6482.35612 19767.163
## 1999.069       6653.533 -2044.27565 15351.342  -6648.61744 19955.684
## 1999.073       6664.663 -2149.65365 15478.979  -6815.67083 20144.996
## 1999.077       6675.792 -2255.54727 15607.132  -6983.51279 20335.097
## 1999.081       6686.922 -2361.95425 15735.798  -7152.13985 20525.983
## 1999.085       6698.051 -2468.87234 15864.975  -7321.54860 20717.651
## 1999.088       6709.181 -2576.29936 15994.661  -7491.73568 20910.097
## 1999.092       6720.310 -2684.23311 16124.854  -7662.69775 21103.319
## 1999.096       6731.440 -2792.67146 16255.552  -7834.43153 21297.312
## 1999.100       6742.570 -2901.61228 16386.751  -8006.93378 21492.073
## 1999.104       6753.699 -3011.05348 16518.452  -8180.20129 21687.600
## 1999.108       6764.829 -3120.99299 16650.650  -8354.23091 21883.888
## 1999.112       6775.958 -3231.42877 16783.345  -8529.01949 22080.936
## 1999.115       6787.088 -3342.35880 16916.535  -8704.56397 22278.740
## 1999.119       6798.217 -3453.78109 17050.216  -8880.86130 22477.296
## 1999.123       6809.347 -3565.69366 17184.388  -9057.90845 22676.603
## 1999.127       6820.477 -3678.09458 17319.048  -9235.70245 22876.656
## 1999.131       6831.606 -3790.98191 17454.194  -9414.24037 23077.453
## 1999.135       6842.736 -3904.35377 17589.825  -9593.51930 23278.991
## 1999.138       6853.865 -4018.20826 17725.939  -9773.53636 23481.267
## 1999.142       6864.995 -4132.54353 17862.533  -9954.28871 23684.278
## 1999.146       6876.124 -4247.35776 17999.607 -10135.77355 23888.022
## 1999.150       6887.254 -4362.64911 18137.157 -10317.98810 24092.496
## 1999.154       6898.384 -4478.41580 18275.183 -10500.92962 24297.697
## 1999.158       6909.513 -4594.65606 18413.682 -10684.59539 24503.622
## 1999.162       6920.643 -4711.36813 18552.654 -10868.98274 24710.268
## 1999.165       6931.772 -4828.55028 18692.095 -11054.08900 24917.634
## 1999.169       6942.902 -4946.20078 18832.005 -11239.91156 25125.715
## 1999.173       6954.031 -5064.31795 18972.381 -11426.44782 25334.511
## 1999.177       6965.161 -5182.90010 19113.222 -11613.69520 25544.017
## 1999.181       6976.291 -5301.94557 19254.527 -11801.65118 25754.232
## 1999.185       6987.420 -5421.45272 19396.293 -11990.31324 25965.154
## 1999.188       6998.550 -5541.41993 19538.519 -12179.67888 26176.778
## 1999.192       7009.679 -5661.84558 19681.204 -12369.74566 26389.104
## 1999.196       7020.809 -5782.72808 19824.346 -12560.51113 26602.129
## 1999.200       7031.938 -5904.06586 19967.943 -12751.97289 26815.850
## 1999.204       7043.068 -6025.85735 20111.993 -12944.12854 27030.265
## 1999.208       7054.198 -6148.10102 20256.496 -13136.97574 27245.371
## 1999.212       7065.327 -6270.79533 20401.450 -13330.51214 27461.166
## 1999.215       7076.457 -6393.93878 20546.852 -13524.73543 27677.649
## 1999.219       7087.586 -6517.52987 20692.702 -13719.64332 27894.816
## 1999.223       7098.716 -6641.56710 20838.999 -13915.23354 28112.665
#library(prophet)
#stocks <- as.data.frame(EuStockMarkets[,4])
#summary(stocks)
#pro_time <- time(EuStockMarkets[,4])
#pro_ftse <- EuStockMarkets[,4]
#head(pro_time)
#df <- data.frame (
#  ds = as.POSIXct(pro_time, format="%Y-%m-%d", tz="UTC"),
#  y = pro_ftse
#)
#summary(df)
#modpro <- prophet(df)
#forecaste_pro_ftse <- make_future_dataframe(modpro, 100)
#plot(forecaste_pro_ftse, main = "Graph with forecasting of ftse",col.main = "darkgreen")